Solved Exercises on Solving Problems Using Data in Grade 3

Master solving problems using data: analyzing data from various sources to solve mathematical word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition Using Data
Exercise 1
The school library has a bar graph showing books checked out by genre: Fiction = 24 books, Non-fiction = 18 books, Mystery = 15 books, Biography = 12 books. How many books were checked out in total? If 10 more fiction books are checked out tomorrow, how many fiction books will there be?
Definition:

Solving problems using data: Using information from graphs, charts, or tables to answer mathematical questions.

Addition: Combining numbers to find a total amount.

Problem solving method:
  1. Read the problem carefully
  2. Identify the data needed
  3. Extract values from the source
  4. Perform the required mathematical operation
  5. Check your answer
24
Fiction
18
Non-fiction
15
Mystery
12
Biography
0
5
10
15
20
24
Fiction:
24 books
Non-fiction:
18 books
Mystery:
15 books
Biography:
12 books
1 Find total books: 24 + 18 + 15 + 12 = 69 books
2 Add more fiction: 24 + 10 = 34 fiction books
Step 1: Identify the data needed

All four genres of books

Step 2: Extract values from graph

Fiction = 24, Non-fiction = 18, Mystery = 15, Biography = 12

Step 3: Add for total

24 + 18 + 15 + 12 = 69 books total

Step 4: Add additional fiction books

Original fiction: 24, Additional: 10, Total: 24 + 10 = 34

Final answer:

69 books were checked out in total

There will be 34 fiction books after tomorrow

Applied rules:

• Data extraction: Accurately read values from the graph

• Addition: Combine all values for total

• Sequential calculation: Handle multiple parts of the question

2 Subtraction Using Data
Exercise 2
A picture graph shows the number of stickers each student earned. Each 🌟 represents 3 stickers. Students: Alice = 🌟🌟🌟, Bob = 🌟🌟, Carol = 🌟🌟🌟🌟, David = 🌟. How many more stickers did Carol earn than David? If Alice gives 6 stickers to David, how many stickers does Alice have left?
Definition:

Subtraction: Finding the difference between two amounts or taking away from a total.

Symbol value: What each picture represents in a picture graph.

Problem solving method:
  1. Identify the symbol key
  2. Count symbols for each category
  3. Calculate actual values
  4. Perform required operations
  5. Answer the question
9
🌟🌟🌟
Alice
6
🌟🌟
Bob
12
🌟🌟🌟🌟
Carol
3
🌟
David
0
3
6
9
12
Alice:
3 symbols × 3 = 9 stickers
Bob:
2 symbols × 3 = 6 stickers
Carol:
4 symbols × 3 = 12 stickers
David:
1 symbol × 3 = 3 stickers
1 Carol vs David: 12 - 3 = 9 more stickers
2 Alice after giving: 9 - 6 = 3 stickers
Step 1: Apply symbol key to each student

Alice: 3 × 3 = 9, Bob: 2 × 3 = 6, Carol: 4 × 3 = 12, David: 1 × 3 = 3

Step 2: Calculate difference between Carol and David

12 - 3 = 9 more stickers

Step 3: Calculate Alice's remaining stickers

Original: 9, Given away: 6, Remaining: 9 - 6 = 3

Final answer:

Carol earned 9 more stickers than David

Alice has 3 stickers left after giving 6 to David

Applied rules:

• Symbol multiplication: Always apply the key value

• Subtraction for comparison: Larger value minus smaller value

• Takeaway subtraction: Original amount minus amount given away

3 Comparison Using Data
Exercise 3
A line plot shows the number of minutes students spent reading: 10 min (2 dots), 15 min (4 dots), 20 min (3 dots), 25 min (1 dot). How many students read for 15 minutes? How many more students read for 15 minutes than 25 minutes? What fraction of students read for 20 minutes?
Definition:

Comparison: Looking at different values to see how they relate to each other.

Fraction: A part of a whole expressed as numerator over denominator.

Problem solving method:
  1. Count dots for each value
  2. Calculate total participants
  3. Perform comparisons as needed
  4. Express parts as fractions
2
●●
10
4
●●●●
15
3
●●●
20
1
●
25
10
15
20
25
10 min:
2 students
15 min:
4 students
20 min:
3 students
25 min:
1 student
1 Students reading 15 min: 4 students
2 Difference: 4 - 1 = 3 more students
3 Total students: 2 + 4 + 3 + 1 = 10
4 Fraction: 3/10 of students read 20 min
Step 1: Count students for each reading time

10 min: 2 students, 15 min: 4 students, 20 min: 3 students, 25 min: 1 student

Step 2: Answer first question

4 students read for 15 minutes

Step 3: Calculate difference between 15 and 25 min

4 - 1 = 3 more students

Step 4: Calculate fraction for 20 min readers

Students reading 20 min: 3, Total students: 10, Fraction: 3/10

Final answer:

4 students read for 15 minutes

3 more students read for 15 minutes than 25 minutes

3/10 of students read for 20 minutes

Applied rules:

• Dot counting: Count each dot above each value

• Subtraction for comparison: Larger value minus smaller value

• Fraction formation: Part over total

Problem Solving Using Data Concepts and Methods
📊 Solution = Data + Operation
Problem Solving Formula
📊
Data Sources: Graphs, charts, tables, surveys
🔍
Operations: Add, subtract, multiply, divide
🎯
Problem Steps: Read, extract, calculate, answer
Key definitions:

Solving problems using data: Using information from graphs, charts, or tables to answer mathematical questions.

Data extraction: Finding and taking specific information from a data source.

Mathematical operations: Addition, subtraction, multiplication, and division used to solve problems.

Comparison: Looking at different values to see how they relate to each other.

Fraction: A way to express part of a whole (numerator/denominator).

Problem Solving Process:
  1. Read carefully: Understand what the problem is asking
  2. Identify data: Find where the needed information is located
  3. Extract values: Take the specific numbers from the data source
  4. Choose operation: Decide which mathematical operation to use
  5. Calculate: Perform the mathematical computation
  6. Check: Verify that your answer makes sense
Tip 1: Always read the entire problem before looking at the data.
Tip 2: Circle or underline key numbers and words in the problem.
Tip 3: Double-check that you extracted the correct values from the data.
Common errors: Misreading data, using wrong values, choosing incorrect operations, calculation mistakes.
Key points: Careful reading, accurate data extraction, correct operations, verification.
Important Rules:

• Always read the problem completely first

• Extract data accurately from sources

• Choose the right mathematical operation

• Check your work for accuracy

• Make sure your answer makes sense

Solution: Exercises 4 to 5
4 Multi-Step Problem Solving
Exercise 4
A class survey shows favorite fruits: Apples = 15 students, Bananas = 12 students, Oranges = 8 students, Grapes = 10 students. If 3 more students join the class and all choose apples, and 2 students change their vote from bananas to oranges, how many students now prefer apples? What is the new difference between apple and banana lovers?
Definition:

Multi-step problems: Questions requiring multiple operations to solve.

15
Apples
12
Bananas
8
Oranges
10
Grapes
0
5
10
15
1 Initial counts: Apples = 15, Bananas = 12
2 New apple lovers: 15 + 3 = 18
3 New banana lovers: 12 - 2 = 10
4 Difference: 18 - 10 = 8
Step 1: Identify initial values

Apples: 15, Bananas: 12, Oranges: 8, Grapes: 10

Step 2: Calculate new apple count

Original: 15, Added: 3, New total: 15 + 3 = 18

Step 3: Calculate new banana count

Original: 12, Moved away: 2, New total: 12 - 2 = 10

Step 4: Find the new difference

Apples: 18, Bananas: 10, Difference: 18 - 10 = 8

Final answer:

18 students now prefer apples

The new difference between apple and banana lovers is 8 students

Applied rules:

• Sequential updates: Apply changes step by step

• Addition for increases: Add new members to existing count

• Subtraction for decreases: Subtract moved members

5 Complex Data Analysis
Exercise 5
A school collects data on lunch preferences over 4 days: Monday = 45 students, Tuesday = 38 students, Wednesday = 52 students, Thursday = 41 students. If the cafeteria wants to prepare enough food for the average number of students over these 4 days, rounded up to the nearest ten, how much food should they prepare? What percent more students ate on Wednesday compared to Tuesday?
Definition:

Average: The sum of all values divided by the number of values.

Percent increase: The difference between two values expressed as a percentage of the original value.

45
Mon
38
Tue
52
Wed
41
Thu
0
10
20
30
40
50
1 Total students: 45 + 38 + 52 + 41 = 176
2 Average: 176 ÷ 4 = 44
3 Rounded up to nearest 10: 50
4 Wednesday vs Tuesday: (52 - 38) ÷ 38 × 100 = 36.8%
Step 1: Calculate total students over 4 days

45 + 38 + 52 + 41 = 176 students total

Step 2: Calculate the average

176 ÷ 4 = 44 students per day

Step 3: Round up to nearest ten

44 rounded up to nearest ten is 50

Step 4: Calculate percent increase from Tuesday to Wednesday

Difference: 52 - 38 = 14, Percent: (14 ÷ 38) × 100 = 36.8%

Final answer:

The cafeteria should prepare food for 50 students

36.8% more students ate on Wednesday compared to Tuesday

Applied rules:

• Average calculation: Sum ÷ Count

• Rounding up: Round to next higher multiple of specified number

• Percent increase: (New - Old) ÷ Old × 100

Comprehensive Problem Solving Using Data Guide: Definitions, Rules, and Methods
📊 Average = Sum ÷ Count
Average Calculation Rule
Key definitions:

Solving problems using data: Using information from graphs, charts, or tables to answer mathematical questions.

Data extraction: Finding and taking specific information from a data source.

Mathematical operations: Addition, subtraction, multiplication, and division used to solve problems.

Average: The sum of all values divided by the number of values.

Comparison: Looking at different values to see how they relate to each other.

Fraction: A way to express part of a whole (numerator/denominator).

Percent: A ratio expressed as a fraction of 100.

Complete Problem Solving Methodology:
  1. Understand: Read the problem carefully and identify what is being asked
  2. Locate: Find where the needed data is presented
  3. Extract: Carefully take the specific values from the data source
  4. Plan: Decide which mathematical operations to use
  5. Calculate: Perform the mathematical computations
  6. Verify: Check that your answer makes sense in the context
  7. Answer: Provide a complete response to the question
Tip 1: Always read the entire problem before looking at the data to understand what you need to find.
Tip 2: Use scratch paper to organize your calculations and keep track of numbers.
Tip 3: Check that your answer is reasonable by comparing it to the original data.
Tip 4: For multi-step problems, solve one step at a time and keep track of your results.
Common errors: Misreading data, using wrong values, choosing incorrect operations, calculation mistakes, not checking answers.
Exam preparation: Practice different problem types, focus on multi-step problems, work on word problem comprehension.
Essential Rules and Laws:

• Read completely: Understand the problem before extracting data

• Accurate extraction: Take correct values from data sources

• Correct operations: Use the appropriate mathematical operation

• Verification: Check that answers make sense in context

• Complete answers: Address all parts of the question

1
Understand: Read problem and identify what's being asked
2
Locate: Find where needed data is presented
3
Extract: Carefully take specific values
4
Plan: Decide which operations to use
5
Calculate: Perform mathematical computations
6
Verify: Check that answer makes sense

Questions & Answers

Question: I get confused about which operation to use when solving problems with data. How do I know when to add, subtract, multiply, or divide?

Answer: Here's how to identify the right operation:

  • Addition (+): When you see words like "total," "altogether," "sum," "combined," "in all"
  • Subtraction (-): When you see words like "difference," "more than," "less than," "remains," "decreased by"
  • Multiplication (×): When you see words like "each," "per," "product," "times," "groups of"
  • Division (÷): When you see words like "average," "per," "out of," "ratio," "split equally"

Read the question carefully and look for these clue words to help you choose the right operation!

Question: My child struggles with multi-step problems. How can I help them break these down?

Answer: Try this approach:

  • Read together: Go through the problem multiple times
  • Highlight key info: Circle numbers and important words
  • Break it down: Identify each separate question within the problem
  • Solve step-by-step: Complete one part before moving to the next
  • Check progress: Verify each step before continuing

Encourage your child to write down each step and keep their work organized.

Question: What does "rounded up to the nearest ten" mean?

Answer: Rounding up means going to the next higher multiple of 10:

  • If you have 44, rounding up to nearest 10 gives you 50
  • If you have 32, rounding up to nearest 10 gives you 40
  • If you have 50, it stays 50 (already a multiple of 10)

"Rounding up" always goes to the next higher multiple, even if the number is already close to the next one!